{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# The Curse of Dimensionality"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "An increase in the number of dimensions of a dataset means that there are more entries in the vector of features that represents each observation in the corresponding Euclidean space. We measure the distance in a vector space using Euclidean distance, also known as L2 norm, which we applied to the vector of linear regression coefficients to train a regularized Ridge Regression model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Euclidean distance between two n-dimensional vectors with Cartesian coordinates p = (p1, p2, ..., pn) and q = (q1, q2, ..., qn) is computed using the familiar formula developed by Pythagoras:\n",
    "$$d(p, q)=\\sqrt{\\sum_{i=1}^n(p_i−q_i)^2}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Hence, each new dimension adds a non-negative term to the sum, so that the distance increases with the number of dimensions for distinct vectors. In other words, as the number of features grows for a given number of observations, the feature space becomes increasingly sparse, i.e., less dense or emptier. On the flip side, the lower data density requires more observations to keep the average distance between data points the same."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-12-27T18:09:59.348731Z",
     "start_time": "2018-12-27T18:09:59.333204Z"
    },
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "from numpy import clip, full, fill_diagonal\n",
    "from numpy.random import uniform, multivariate_normal, seed\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.spatial.distance import pdist, squareform\n",
    "\n",
    "%matplotlib inline\n",
    "pd.options.display.float_format = '{:,.2f}'.format\n",
    "seed(42)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Simulate pairwise distances of points in $\\mathbb{R}^n$ (while $n$ increases)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The simulation draws features in the range [0, 1] from uncorrelated uniform or correlated normal distributions and gradually increases the number of features to 2,500. \n",
    "\n",
    "The average distance between data points increases to over 11 times the feature range for features drawn from the normal distribution, and to over 20 times in the (extreme) case of uncorrelated uniform distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-11-12T17:01:27.853523Z",
     "start_time": "2018-11-12T17:01:27.842853Z"
    }
   },
   "outputs": [],
   "source": [
    "def get_distance_metrics(points):\n",
    "    \"\"\"Calculate mean of pairwise distances and \n",
    "        mean of min pairwise distances\"\"\"\n",
    "    pairwise_dist = squareform(pdist(points))\n",
    "    fill_diagonal(pairwise_dist, np.nanmean(pairwise_dist, axis=1))\n",
    "    avg_distance = np.mean(np.nanmean(pairwise_dist, axis=1))\n",
    "    fill_diagonal(pairwise_dist, np.nanmax(pairwise_dist, axis=1))\n",
    "    avg_min_distance = np.mean(np.nanmin(pairwise_dist, axis=1))\n",
    "    return avg_distance, avg_min_distance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-11-12T17:01:28.213829Z",
     "start_time": "2018-11-12T17:01:28.203262Z"
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "def simulate_distances(m, n, mean, var, corr):\n",
    "    \"\"\"Draw m random vectors of dimension n \n",
    "        from uniform and normal distributions\n",
    "        and return pairwise distance metrics\"\"\"\n",
    "    uni_dist = get_distance_metrics(uniform(size=(m, n)))\n",
    "    cov = full(shape=(n, n), fill_value=var * corr)\n",
    "    fill_diagonal(cov, var)\n",
    "    normal_points = multivariate_normal(\n",
    "        full(shape=(n,), fill_value=mean), cov, m)\n",
    "    normal_points = clip(normal_points, a_min=0, a_max=1)\n",
    "    norm_dist = get_distance_metrics(normal_points)\n",
    "    return uni_dist, norm_dist"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-11-12T17:02:21.554155Z",
     "start_time": "2018-11-12T17:01:28.594384Z"
    },
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "# sampling params\n",
    "n_points = 1000\n",
    "min_dim, max_dim, step = 1, 2502, 100 # from 1 - 2501\n",
    "dimensions = range(min_dim, max_dim, step)\n",
    "\n",
    "# normal distribution params\n",
    "mean = 0.5 \n",
    "var = (mean/3)**2 # 99% of sample in [0, 1]\n",
    "corr = 0.25\n",
    "\n",
    "# run simulation\n",
    "avg_dist = []\n",
    "for dim in dimensions:\n",
    "    uni_dist, norm_dist  = simulate_distances(\n",
    "        n_points, dim, mean, var, corr)\n",
    "    avg_dist.append([*uni_dist, *norm_dist])\n",
    "    \n",
    "col_names = ['Avg. Uniform', 'Min. Uniform',\n",
    "             'Avg. Normal', 'Min. Normal']\n",
    "distances = pd.DataFrame(data=avg_dist,  \n",
    "            columns=col_names, index=dimensions)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-11-12T17:07:01.736151Z",
     "start_time": "2018-11-12T17:07:00.667977Z"
    },
    "hide_input": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1008x576 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "title = 'Distance of {:,.0f} Data Points in a Unit Hypercube'.format(n_points)\n",
    "fig, axes = plt.subplots(nrows=2, ncols=1, figsize=(14, 8))\n",
    "distances[[ 'Avg. Uniform', 'Avg. Normal']].plot.bar(title='Average ' + title, ax=axes[0])\n",
    "distances[[ 'Min. Uniform', 'Min. Normal']].plot.bar(title='Minimum ' + title, ax=axes[1])\n",
    "\n",
    "for ax in axes:\n",
    "    ax.grid(axis='y', lw=1, ls='--')\n",
    "    for p in ax.patches:\n",
    "        ax.annotate('{:.1f}'.format(p.get_height()), (p.get_x() + .005, p.get_height() + .25), fontsize=10)\n",
    "fig.tight_layout();"
   ]
  }
 ],
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   "display_name": "Python 3",
   "language": "python",
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  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.0"
  },
  "toc": {
   "base_numbering": 1,
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   "number_sections": true,
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   "skip_h1_title": true,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
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   "toc_position": {},
   "toc_section_display": true,
   "toc_window_display": true
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}
